Question

how to find dual basis?

Answer 1

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I(the cardinality of I is the dimensionality of V), its dual set is a set B∗ of vectors in the dual space V∗ with the same index set I such that Band B∗ form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V∗. If it does span V∗, then B∗ is called the dual basis or reciprocal basis for the basis B.